document.write( "Question 299535: trial factoring or reverse foil\r
\n" ); document.write( "\n" ); document.write( "x^2+8x-20 \n" ); document.write( "

Algebra.Com's Answer #215210 by jim_thompson5910(35256) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "Looking at the expression $\"x%5E2%2B8x-20\"$ , we can see that the first coefficient is $\"1\"$ , the second coefficient is $\"8\"$ , and the last term is $\"-20\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient $\"1\"$ by the last term $\"-20\"$ to get $\"%281%29%28-20%29=-20\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now the question is: what two whole numbers multiply to $\"-20\"$ (the previous product) and add to the second coefficient $\"8\"$ ?\r
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\n" ); document.write( "\n" ); document.write( "To find these two numbers, we need to list all of the factors of $\"-20\"$ (the previous product).\r
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\n" ); document.write( "\n" ); document.write( "Factors of $\"-20\"$ :\r
\n" ); document.write( "\n" ); document.write( "1,2,4,5,10,20\r
\n" ); document.write( "\n" ); document.write( "-1,-2,-4,-5,-10,-20\r
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\n" ); document.write( "\n" ); document.write( "Note: list the negative of each factor. This will allow us to find all possible combinations.\r
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\n" ); document.write( "\n" ); document.write( "These factors pair up and multiply to $\"-20\"$ .\r
\n" ); document.write( "\n" ); document.write( "1*(-20) = -20
\n" ); document.write( "2*(-10) = -20
\n" ); document.write( "4*(-5) = -20
\n" ); document.write( "(-1)*(20) = -20
\n" ); document.write( "(-2)*(10) = -20
\n" ); document.write( "(-4)*(5) = -20\r
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\n" ); document.write( "\n" ); document.write( "Now let's add up each pair of factors to see if one pair adds to the middle coefficient $\"8\"$ :\r
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First Number	Second Number	Sum
1	-20	1+(-20)=-19
2	-10	2+(-10)=-8
4	-5	4+(-5)=-1
-1	20	-1+20=19
-2	10	-2+10=8
-4	5	-4+5=1

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\n" ); document.write( "\n" ); document.write( "From the table, we can see that the two numbers $\"-2\"$ and $\"10\"$ add to $\"8\"$ (the middle coefficient).\r
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\n" ); document.write( "\n" ); document.write( "So the two numbers $\"-2\"$ and $\"10\"$ both multiply to $\"-20\"$ and add to $\"8\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now replace the middle term $\"8x\"$ with $\"-2x%2B10x\"$ . Remember, $\"-2\"$ and $\"10\"$ add to $\"8\"$ . So this shows us that $\"-2x%2B10x=8x\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"x%5E2%2Bhighlight%28-2x%2B10x%29-20\"$ Replace the second term $\"8x\"$ with $\"-2x%2B10x\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"%28x%5E2-2x%29%2B%2810x-20%29\"$ Group the terms into two pairs.\r
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\n" ); document.write( "\n" ); document.write( " $\"x%28x-2%29%2B%2810x-20%29\"$ Factor out the GCF $\"x\"$ from the first group.\r
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\n" ); document.write( "\n" ); document.write( " $\"x%28x-2%29%2B10%28x-2%29\"$ Factor out $\"10\"$ from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.\r
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\n" ); document.write( "\n" ); document.write( " $\"%28x%2B10%29%28x-2%29\"$ Combine like terms. Or factor out the common term $\"x-2\"$ \r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So $\"x%5E2%2B8x-20\"$ factors to $\"%28x%2B10%29%28x-2%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "In other words, $\"x%5E2%2B8x-20=%28x%2B10%29%28x-2%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Note: you can check the answer by expanding $\"%28x%2B10%29%28x-2%29\"$ to get $\"x%5E2%2B8x-20\"$ or by graphing the original expression and the answer (the two graphs should be identical).
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